The determinants of q-distance matrices of trees and two quantities relating to permutations
主 题: The determinants of q-distance matrices of trees and two quantities relating to permutations
报告人: 葉永南 教授 (Academia Sinica, Taipei)
时 间: 2015-09-09 16:00-17:00
地 点: 理科一号楼 1569
Graham and Pollak [Bell System Tech. J. 50 (1971) 2495–2519] obtained a beautiful formula on the determinant of distance matrices of trees, which is independent of the structure of the trees. In this talk we give a simple proof of Graham and Pollak's result. We also prove that two quantities relating to the length of permutations defined on trees are independent of the structures of trees. We also find that these results are closely related to the results obtained by Bapat, Kirkland, and Neumann [R. Bapat, S.J. Kirkland, M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193–209].